This invention relates to removing noise from the digitized output of a sensor, the sensor being subject to undesired (although perhaps necessary) internal or external resonance. It further relates to such removal when the resonant frequency is unknown or drifts.
A popular form of angular rate sensor includes a piezoelectric tuning fork. When the fork is rotated, coriolis forces distort the fork proportionally to the magnitude of the rotation. Effects of resonance of the tuning fork, however, must be removed from the output signal from the fork. This is possible, with a notch filter, if the effect is at a frequency removed from the frequency of interest by an order of magnitude. This is often the case.
In the foregoing example, the resonance is internal to the sensor. It is equally desirable to remove resonance-induced noise from the output of a sensor even when the resonance is external to the sensor. This would occur, for example, in electrical equipment powered by an unstable supply. 60-cycle hum from commercially supplied electricity is easily notched out, but the unstable output of an emergency generator can make its way into a signal to be measured, and is much more difficult to remove. Again, the resonant frequency (and its effect) must be at a frequency somewhat removed from the frequency of interest.
We return to the angular rate sensor with an underlying operating frequency which must be removed from its output signal. This removal is relatively straightforward with a (digital) stagger-tuned notch filter when the frequency range is somewhat known. Stagger-tuned notch filters, however, introduce considerable phase lag.
When the frequency is grossly unknown, unstable, or both, stagger-tuned filters introduce so much phase lagxe2x80x94even at frequencies at some distance below the notch frequencyxe2x80x94as to make them unsuitable for an important application: closed-loop control. The solution is to use a very narrow adaptive notch filter, the very narrowness of which greatly reduces phase lag. However, a very narrow notch filter must be an infinite impulse response (IIR) filter; it must be recursive. This in turn makes the adaptive tracking of the notch frequency of the filter unstable: there are many relative minima on the performance-criterion surface. This in turn makes it unsuitable for closed-loop control.
What is needed is an IIR filter to notch out the objectionable resonance with the stable adaptive properties of a non-recursive, finite impulse response (FIR) filter. This problem seems insoluble.
Applicants have solved the problem by noting a hidden distinction in the statement of the problem. The very narrow notch filter which removes the resonance-induced noise must have a low phase delay and therefore must be recursive. However, the apparatus which determines the center frequency of the notch filter may be non-recursive, and therefore stable.
This center-frequency apparatus includes a tunable FIR filter which tracks the same resonance that we wish the IIR filter to remove; that is, the numerator of its transfer function has zeroes at the same values. Most of the energy of the input signal is in the resonant noise, not the measurement of the parameter. Tuning the FIR filter to minimize the output of the FIR filter therefore tunes the notch frequency to align with the resonant frequency. The tuning parameter which adaptively produces this result is suitably scaled and biased, and is applied to the IIR filter, the numerator of whose transfer function is precisely the same as that of the transfer function of the FIR filter. Because the tuning parameter was adaptively generated in an FIR filter, it is stable. Because it is applied to an IIR filter to filter the raw output of the sensor, the raw output is filtered without significant phase delay.
The foregoing assumes that the resonant frequency, to be notched out, drifts relatively slowly. This is usually the case. If the resonant frequency drifts rapidly, then the phase delay inherent in the emulating FIR filter will not allow the tuning parameter to drift quickly enough to follow it. If this happens, unacceptably large amounts of resonant frequency noise will be passed by the IIR filter. The present invention should not be used in such situations.